constructive interference

Meaning: When waves overlap, their displacements add at each point (superposition). If crests meet crests and troughs meet troughs, the waves are in phase and the resultant amplitude is the sum of the individual amplitudes. For two equal waves the amplitude doubles. Interference changes where energy goes, but the total energy is not created, since it is redistributed between bright and dark (or loud and quiet) regions.

Equation: Path difference condition for two coherent sources in phase: ΔL = mλ, where ΔL is the path difference (m), m = 0, 1, 2, … is an integer, and λ is the wavelength (m). The phase difference is then Δφ = 2πm (radians).

On the MCAT: Typical setups are Young's double slit (bright fringes where d sinθ = mλ, with d the slit spacing in m), thin films, sound from two speakers (louder spots), and beats. You may be asked to predict whether a point is loud or quiet, bright or dark, given path lengths and wavelength. Check for a phase shift on reflection, such as light reflecting off a higher-index medium, because this can flip the condition.

Common confusion: Students think constructive interference means the waves are the same and destructive means they cancel permanently. The waves pass through each other unchanged afterward. Also, a half-wavelength path difference (λ/2, 3λ/2) gives destructive interference, not constructive, when the sources are in phase.